基于变步长离散随机集的风险不确定性分析方法

针对信息不一致、不完整下的风险评估不确定性难以刻画与传播问题，提出一种基于变步长离散随机集理论的风险混合不确定性分析方法。将各类不完整、不精确信息转化为随机集刻画框架，在随机集理论框架下建立了统一的混合不确定性传播模型，利用随机扩张原理，计算出风险的不确定性包络曲线。为解决不一致冲突信息的不确定性合成，采用D-S证据合成原则实现多源不确定性的融合。为减小不确定性传播截尾相对误差，提出一种不确定性变量分布的变步长离散随机集刻画策略，并给出了基于变步长离散随机集理论的混合不确定性传播实施步骤。通过一个质量-弹簧-阻尼非线性物理与现象响应模型，验证了方法的有效性和可用性。

Analysis method on risk uncertainty based on variable step discrete random set

In view of hybrid uncertainty presentation and propagation considering the dissonance and im-precision of information in risk assessment, a hybrid uncertainty analysis method based on variable step dis-crete random set theory was proposed.All kinds of incomplete and dissonant knowledge was represented with random set framework,a unified hybrid uncertainty propagation model was built using random extension princi -ple,and uncertainty envelope curvesof risk was calculated at the same time.To solve the uncertainty combina-tion problem of dissonant and conflict informations, D-S evidence combination principle was used to merge multisource uncertainty informations.For reducing the tail relative error, a variable step discrete random set presentation strategy of uncertainty variables was proposed, and the analysis procedure of hybrid uncertainty propagation was put forward based on variable step discrete random set theory.In conclusion, a physics and phenomena response model of a mass-spring-damper system was taken to verify the effectiveness and feasibility of the proposed method.